Reverse engineering of logic-based differential equation models using a mixed-integer dynamic optimization approach

9 páginas, 6 figuras.-- This is an Open Access article distributed under the terms of the Creative Commons Attribution LicenseMotivation: Systems biology models can be used to test new hypotheses formulated on the basis of previous knowledge or new experimental data, contradictory with a previously existing model. New hypotheses often come in the shape of a set of possible regulatory mechanisms. This search is usually not limited to finding a single regulation link, but rather a combination of links subject to great uncertainty or no information about the kinetic parameters. Results: In this work, we combine a logic-based formalism, to describe all the possible regulatory structures for a given dynamic model of a pathway, with mixed-integer dynamic optimization (MIDO). This framework aims to simultaneously identify the regulatory structure (represented by binary parameters) and the real-valued parameters that are consistent with the available experimental data, resulting in a logic-based differential equation model. The alternative to this would be to perform real-valued parameter estimation for each possible model structure, which is not tractable for models of the size presented in this work. The performance of the method presented here is illustrated with several case studies: a synthetic pathway problem of signaling regulation, a two-component signal transduction pathway in bacterial homeostasis, and a signaling network in liver cancer cellsD.H., J.R.B. and J.S.R. acknowledge funding from the EU FP7 projects ‘NICHE’ (ITN Grant number 289384) and ‘BioPreDyn’ (KBBE grant number 289434). J.R.B. also acknowledges funding from the Spanish Ministerio de Economía y Competitividad (and the FEDER) through the project MultiScales (DPI2011-28112-C04-03).Peer reviewe

Augmented Sparse Reconstruction of Protein Signaling Networks

The problem of reconstructing and identifying intracellular protein signaling and biochemical networks is of critical importance in biology today. We sought to develop a mathematical approach to this problem using, as a test case, one of the most well-studied and clinically important signaling networks in biology today, the epidermal growth factor receptor (EGFR) driven signaling cascade. More specifically, we suggest a method, augmented sparse reconstruction, for the identification of links among nodes of ordinary differential equation (ODE) networks from a small set of trajectories with different initial conditions. Our method builds a system of representation by using a collection of integrals of all given trajectories and by attenuating block of terms in the representation itself. The system of representation is then augmented with random vectors, and minimization of the 1-norm is used to find sparse representations for the dynamical interactions of each node. Augmentation by random vectors is crucial, since sparsity alone is not able to handle the large error-in-variables in the representation. Augmented sparse reconstruction allows to consider potentially very large spaces of models and it is able to detect with high accuracy the few relevant links among nodes, even when moderate noise is added to the measured trajectories. After showing the performance of our method on a model of the EGFR protein network, we sketch briefly the potential future therapeutic applications of this approach.Comment: 24 pages, 6 figure

Data-driven reverse engineering of signaling pathways using ensembles of dynamic models

Signaling pathways play a key role in complex diseases such as cancer, for which the development of novel therapies is a difficult, expensive and laborious task. Computational models that can predict the effect of a new combination of drugs without having to test it experimentally can help in accelerating this process. In particular, network-based dynamic models of these pathways hold promise to both understand and predict the effect of therapeutics. However, their use is currently hampered by limitations in our knowledge of the underlying biochemistry, as well as in the experimental and computational technologies used for calibrating the models. Thus, the results from such models need to be carefully interpreted and used in order to avoid biased predictions. Here we present a procedure that deals with this uncertainty by using experimental data to build an ensemble of dynamic models. The method incorporates steps to reduce overfitting and maximize predictive capability. We find that by combining the outputs of individual models in an ensemble it is possible to obtain a more robust prediction. We report results obtained with this method, which we call SELDOM (enSEmbLe of Dynamic lOgic-based Models), showing that it improves the predictions previously reported for several challenging problems.JRB and DH acknowledge funding from the EU FP7 project NICHE (ITN Grant number 289384). JRB acknowledges funding from the Spanish MINECO project SYNBIOFACTORY (grant number DPI2014-55276-C5-2-R). AFV acknowledges funding from the Galician government (Xunta de Galiza) through the I2C postdoctoral fellowship ED481B2014/133-0. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.info:eu-repo/semantics/publishedVersio

Inference of complex biological networks: distinguishability issues and optimization-based solutions

<p>Abstract</p> <p>Background</p> <p>The inference of biological networks from high-throughput data has received huge attention during the last decade and can be considered an important problem class in systems biology. However, it has been recognized that reliable network inference remains an unsolved problem. Most authors have identified lack of data and deficiencies in the inference algorithms as the main reasons for this situation.</p> <p>Results</p> <p>We claim that another major difficulty for solving these inference problems is the frequent lack of uniqueness of many of these networks, especially when prior assumptions have not been taken properly into account. Our contributions aid the distinguishability analysis of chemical reaction network (CRN) models with mass action dynamics. The novel methods are based on linear programming (LP), therefore they allow the efficient analysis of CRNs containing several hundred complexes and reactions. Using these new tools and also previously published ones to obtain the network structure of biological systems from the literature, we find that, often, a unique topology cannot be determined, even if the structure of the corresponding mathematical model is assumed to be known and all dynamical variables are measurable. In other words, certain mechanisms may remain undetected (or they are falsely detected) while the inferred model is fully consistent with the measured data. It is also shown that sparsity enforcing approaches for determining 'true' reaction structures are generally not enough without additional prior information.</p> <p>Conclusions</p> <p>The inference of biological networks can be an extremely challenging problem even in the utopian case of perfect experimental information. Unfortunately, the practical situation is often more complex than that, since the measurements are typically incomplete, noisy and sometimes dynamically not rich enough, introducing further obstacles to the structure/parameter estimation process. In this paper, we show how the structural uniqueness and identifiability of the models can be guaranteed by carefully adding extra constraints, and that these important properties can be checked through appropriate computation methods.</p

Least-squares methods for identifying biochemical regulatory networks from noisy measurements

&lt;b&gt;Background&lt;/b&gt;: We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks. &lt;b&gt;Results&lt;/b&gt;: The superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and &lt;i&gt;mdm2&lt;/i&gt; messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL)-6 and (IL)-12b messenger RNA expression as a function of ATF3 and NF-κB promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL)-6 and (IL)-12b by ATF3. &lt;b&gt;Conclusion&lt;/b&gt;: The significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable more accurate and reliable identification and modelling of biochemical networks

Reconstruction of the temporal signaling network in Salmonella-infected human cells

Salmonella enterica is a bacterial pathogen that usually infects its host through food sources. Translocation of the pathogen proteins into the host cells leads to changes in the signaling mechanism either by activating or inhibiting the host proteins. Using high-throughput ‘omic’ technologies, changes in the signaling components can be quantified at different levels; however, experimental hits are usually incomplete to represent the whole signaling system as some driver proteins stay hidden within the experimental data. Given that the bacterial infection modifies the response network of the host, more coherent view of the underlying biological processes and the signaling networks can be obtained by using a network modeling approach based on the reverse engineering principles in which a confident region from the protein interactome is found by inferring hits from the omic experiments. In this work, we have used a published temporal phosphoproteomic dataset of Salmonella-infected human cells and reconstructed the temporal signaling network of the human host by integrating the interactome and the phosphoproteomic datasets. We have combined two well-established network modeling frameworks, the Prize-collecting Steiner Forest (PCSF) approach and the Integer Linear Programming (ILP) based edge inference approach. The resulting network conserves the information on temporality, direction of interactions, while revealing hidden entities in the signaling, such as the SNARE binding, mTOR signaling, immune response, cytoskeleton organization, and apoptosis pathways. Targets of the Salmonella effectors in the host cells such as CDC42, RHOA, 14-3-3δ, Syntaxin family, Oxysterol-binding proteins were included in the reconstructed signaling network although they were not present in the initial phosphoproteomic data. We believe that integrated approaches have a high potential for the identification of clinical targets in infectious diseases, especially in the Salmonella infections

Formal methods for Hopfield-like networks.

International audienceBuilding a meaningful model of biological regulatory network is usually done by specifying the components (e.g. the genes) and their interactions, by guessing the values of parameters, by comparing the predicted behaviors to the observed ones, and by modifying in a trial-error process both architecture and parameters in order to reach an optimal fitness. We propose here a different approach to construct and analyze biological models avoiding the trial-error part, where structure and dynamics are represented as formal constraints. We apply the method to Hopfield-like networks, a formalism often used in both neural and regulatory networks modeling. The aim is to characterize automatically the set of all models consistent with all the available knowledge (about structure and behavior). The available knowledge is formalized into formal constraints. The latter are compiled into Boolean formula in conjunctive normal form and then submitted to a Boolean satisfiability solver. This approach allows to formulate a wide range of queries, expressed in a high level language, and possibly integrating formalized intuitions. In order to explore its potential, we use it to find cycles for 3-nodes networks and to determine the flower morphogenesis regulatory network of Arabidopsis thaliana. Applications of this technique are numerous and concern the building of models from data as well as the design of biological networks possessing specified behaviors